Are there any other ways of decomposing 1/11 into sum of two unit fractions? In how many ways can we write 1/60 ass a sum of two unit fractions? More generally, in how many ways can the unit fraction 1/n be written as the sum of two unit fractions? In other word, how many ordered pairs (a, b) of positive integers a, b are there for which 1/n = 1/a + 1/b?
Are there any other ways of decomposing 1/11 into sum of two unit fractions? In how many ways can we write 1/60 ass a sum of two unit fractions? More generally, in how many ways can the unit fraction 1/n be written as the sum of two unit fractions? In other word, how many ordered pairs (a, b) of positive integers a, b are there for which 1/n = 1/a + 1/b?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
A unit fraction is a fraction of the form 1/n where n is a positive integer. Note that the unit fraction can be written as the sum of two fractions in the following three ways:
1/11 = (1/12) + (1/132) = (1/22) + (1/22) = (1/132) + (1/12)
Are there any other ways of decomposing 1/11 into sum of two unit fractions? In how many ways can we write 1/60 ass a sum of two unit fractions? More generally, in how many ways can the unit fraction 1/n be written as the sum of two unit fractions? In other word, how many ordered pairs (a, b) of positive integers a, b are there for which
1/n = 1/a + 1/b?
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